Documentation Verification Report

ZNum

📁 Source: Mathlib/Data/Num/ZNum.lean

Statistics

MetricCount
DefinitionsdecidableDvd, decidableDvd, ZNum, addCommGroup, addMonoid, addMonoidWithOne, commRing, decidableDvd, linearOrder, transfer, transfer_rw
11
Theoremscast_ofZNum, cast_sub', div_to_nat, div_zero, dvd_iff_mod_eq_zero, gcd_to_nat, gcd_to_nat_aux, mem_ofZNum', mod_to_nat, mod_zero, ofInt'_toZNum, ofZNum'_toNat, ofZNum_toNat, pred_succ, sub_to_nat, succ_ofInt', toZNumNeg_succ, toZNum_succ, cast_sub', cast_to_znum, div'_to_nat, divMod_to_nat, divMod_to_nat_aux, mod'_to_nat, to_int_eq_succ_pred, to_nat_eq_succ_pred, abs_toZNum, abs_to_nat, add_one, add_zero, bit0_of_bit0, bit1_of_bit1, cast_add, cast_bit0, cast_bit1, cast_bitm1, cast_inj, cast_le, cast_lt, cast_mul, cast_neg, cast_one, cast_pos, cast_sub, cast_succ, cast_to_int, cast_zero, cast_zero', cast_zneg, cmp_to_int, div_to_int, div_zero, dvd_iff_mod_eq_zero, dvd_to_int, gcd_to_nat, isOrderedAddMonoid, isStrictOrderedRing, le_to_int, lt_to_int, mod_to_int, mul_to_int, neg_of_int, neg_zero, nontrivial, ofInt'_eq, ofInt'_neg, of_intCast, of_natCast, of_nat_toZNum, of_nat_toZNumNeg, of_to_int, of_to_int', to_int_inj, to_of_int, zeroLEOneClass, zero_add, zneg_bit1, zneg_bitm1, zneg_neg, zneg_pos, zneg_pred, zneg_succ, zneg_zneg
83
Total94

Num

Definitions

NameCategoryTheorems
decidableDvd 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
cast_ofZNum 📖mathematicalcastNum
AddMonoidWithOne.toOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
ofZNum
AddMonoidWithOne.toNatCast
castZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
cast_to_nat
ofZNum_toNat
cast_sub' 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
sub'
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
castNum
sub_zero
zero_sub
PosNum.cast_sub'
div_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
Num
instDiv
div_zero
PosNum.div'_to_nat
div_zero 📖mathematicalNum
instDiv
instZeroNum
dvd_iff_mod_eq_zero 📖mathematicalNum
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
CommSemiring.toNonUnitalCommSemiring
commSemiring
instMod
instZeroNum
dvd_to_nat
mod_to_nat
gcd_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
gcd
natSize_to_nat
cast_mul
Nat.size_le
pow_add
mul_lt_mul''
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
IsOrderedRing.toMulPosMono
IsStrictOrderedRing.toIsOrderedRing
Nat.instIsStrictOrderedRing
Nat.lt_size_self
gcd_to_nat_aux
le_of_not_ge
gcd_to_nat_aux 📖mathematicalNum
instLE
natSize
instMul
castNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
gcdAux
not_lt_of_ge
PosNum.natSize_pos
le_to_nat
mod_to_nat
le_of_lt
PosNum.cast_pos
Nat.instIsStrictOrderedRing
natSize_to_nat
mul_to_nat
Nat.size_le
mul_comm
lt_of_mul_lt_mul_right
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
lt_of_le_of_lt
Nat.instAtLeastTwoHAddOfNat
mul_two
mul_add
Distrib.leftDistribClass
add_le_add_right
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
mul_le_mul_right
Nat.instMulLeftMono
le_imp_le_of_le_of_le
le_refl
mul_one
pow_succ
mem_ofZNum' 📖mathematicalNum
ofZNum'
toZNum
mod_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
Num
instMod
mod_zero
PosNum.mod'_to_nat
mod_zero 📖mathematicalNum
instMod
instZeroNum
ofInt'_toZNum 📖mathematicaltoZNum
Num
AddMonoidWithOne.toNatCast
addMonoidWithOne
ZNum.ofInt'
Nat.cast_succ
add_one
toZNum_succ
succ_ofInt'
ZNum.add_one
ofZNum'_toNat 📖mathematicalNum
castNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
ofZNum'
castZNum
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
PosNum.to_nat_to_int
succ'_to_nat
PosNum.succ'_pred'
PosNum.cast_to_nat
ofZNum_toNat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
ofZNum
castZNum
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
PosNum.to_nat_to_int
succ'_to_nat
PosNum.succ'_pred'
PosNum.cast_to_nat
pred_succ 📖mathematicalZNum.succ
ZNum.pred
PosNum.pred'_succ'
ZNum.pred.eq_2
toZNum_succ
succ.eq_1
PosNum.succ'_pred'
toZNum.eq_2
sub_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
Num
instSub
ofZNum_toNat
cast_sub'
to_nat_to_int
succ_ofInt' 📖mathematicalZNum.ofInt'
ZNum
ZNum.instAdd
instOneZNum
ofNat'_succ
add_one
toZNum_succ
ZNum.add_one
ofNat'_zero
toZNumNeg_succ
pred_succ
toZNumNeg_succ 📖mathematicaltoZNumNeg
succ
ZNum.pred
toZNum_succ 📖mathematicaltoZNum
succ
ZNum.succ

PosNum

Definitions

NameCategoryTheorems
decidableDvd 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
cast_sub' 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
sub'
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
castPosNum
sub'_one
Num.cast_toZNum
Num.cast_to_nat
pred'_to_nat
Nat.cast_sub
Nat.instIsStrictOrderedRing
cast_to_nat
Nat.cast_one
one_sub'
Num.cast_toZNumNeg
neg_sub
sub'.eq_3
ZNum.cast_bit0
add_left_comm
add_assoc
Int.cast_add
cast_to_int
Int.cast_neg
sub_eq_add_neg
neg_add_rev
AddLeftCancelSemigroup.toIsLeftCancelAdd
sub'.eq_4
ZNum.cast_bitm1
Int.cast_one
add_comm
sub'.eq_5
ZNum.cast_bit1
sub'.eq_6
add_neg_cancel_left
cast_to_znum 📖mathematicalcastPosNum
ZNum
instOneZNum
ZNum.instAdd
ZNum.pos
ZNum.bit0_of_bit0
ZNum.bit1_of_bit1
div'_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
div'
castPosNum
divMod_to_nat
divMod_to_nat 📖mathematicalcastPosNum
Nat.instOne
castNum
MulZeroClass.toZero
Nat.instMulZeroClass
Num
divMod
cast_pos
Nat.instIsStrictOrderedRing
divMod_to_nat_aux
add_zero
MulZeroClass.mul_zero
divMod.eq_def
Nat.instAtLeastTwoHAddOfNat
Num.cast_bit1
two_mul
add_right_comm
mul_left_comm
mul_add
Distrib.leftDistribClass
Num.cast_bit0
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toIsOrderedRing
Nat.instNontrivial
divMod_to_nat_aux 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
castPosNum
Num
divModAux
Num.mem_ofZNum'
Num.cast_toZNum
Num.cast_sub'
sub_eq_iff_eq_add
Num.cast_to_nat
Nat.cast_add
cast_to_nat
Nat.instAtLeastTwoHAddOfNat
Num.cast_bit0
two_mul
lt_of_not_ge
add_comm
Num.to_of_nat
Num.cast_bit1
mul_add
Distrib.leftDistribClass
mul_one
add_assoc
add_lt_add_iff_right
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
mod'_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
mod'
castPosNum
divMod_to_nat
to_int_eq_succ_pred 📖mathematicalcastPosNum
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
castNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
pred'
to_nat_to_int
to_nat_eq_succ_pred
to_nat_eq_succ_pred 📖mathematicalcastPosNum
Nat.instOne
castNum
MulZeroClass.toZero
Nat.instMulZeroClass
pred'
Num.succ'_to_nat
succ'_pred'

ZNum

Definitions

NameCategoryTheorems
addCommGroup 📖CompOp
addMonoid 📖CompOp
addMonoidWithOne 📖CompOp
3 mathmath: of_nat_toZNumNeg, of_natCast, of_nat_toZNum
commRing 📖CompOp
10 mathmath: of_intCast, isOrderedAddMonoid, neg_of_int, to_of_int, dvd_iff_mod_eq_zero, of_to_int, dvd_to_int, cast_sub, isStrictOrderedRing, ofInt'_eq
decidableDvd 📖CompOp
linearOrder 📖CompOp
2 mathmath: isOrderedAddMonoid, isStrictOrderedRing
transfer 📖CompOp
transfer_rw 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
abs_toZNum 📖mathematicalabs
Num.toZNum
abs_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
abs
castZNum
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
PosNum.to_nat_to_int
add_one 📖mathematicalZNum
instAdd
instOneZNum
succ
PosNum.add_one
add_zero 📖mathematicalZNum
instAdd
instZeroZNum
bit0_of_bit0 📖mathematicalZNum
instAdd
bit0
PosNum.bit0_of_bit0
bit1_of_bit1 📖mathematicalZNum
instAdd
instOneZNum
bit1
PosNum.bit1_of_bit1
PosNum.one_sub'
PosNum.bit0_of_bit0
cast_add 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
ZNum
instAdd
zero_add
add_zero
PosNum.cast_add
sub_eq_add_neg
PosNum.cast_sub'
PosNum.cast_to_int
Int.cast_neg
Int.cast_add
add_comm
neg_eq_iff_eq_neg
neg_add_rev
neg_neg
cast_bit0 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
bit0
add_zero
bit0.eq_2
cast_pos
bit0.eq_3
cast_neg
PosNum.cast_bit0
neg_add_rev
cast_bit1 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
bit1
add_zero
zero_add
bit1.eq_2
cast_pos
bit1.eq_3
cast_neg
PosNum.succ'_pred'
add_assoc
neg_add_cancel
Int.cast_neg
PosNum.cast_to_int
add_comm
Int.cast_add
Int.cast_one
neg_add_cancel_left
neg_add_rev
PosNum.cast_succ
AddLeftCancelSemigroup.toIsLeftCancelAdd
cast_bitm1 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
bitm1
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
zneg_zneg
zneg_bit1
cast_zneg
cast_bit1
add_comm
Int.cast_add
cast_to_int
Int.cast_neg
Int.cast_one
add_assoc
neg_add_rev
neg_neg
sub_eq_add_neg
cast_inj 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
cast_to_int
IsStrictOrderedRing.toCharZero
cast_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
castZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
ZNum
instLE
not_lt
cast_lt
cast_lt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
castZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
ZNum
instLT
cast_to_int
Int.cast_lt
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
IsStrictOrderedRing.toZeroLEOneClass
NeZero.charZero_one
IsStrictOrderedRing.toCharZero
lt_to_int
cast_mul 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
ZNum
instMul
Distrib.toMul
cast_to_int
mul_to_int
Int.cast_mul
cast_neg 📖mathematicalcastZNum
neg
castPosNum
cast_one 📖mathematicalcastZNum
ZNum
instOneZNum
cast_pos 📖mathematicalcastZNum
pos
castPosNum
cast_sub 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
AddCommGroupWithOne.toAddCommGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddCommGroupWithOne.toAddGroupWithOne
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommMonoidWithOne.toAddCommMonoid
AddCommGroupWithOne.toAddCommMonoidWithOne
NegZeroClass.toNeg
ZNum
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
commRing
sub_eq_neg_add
cast_add
cast_zneg
cast_succ 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
succ
add_one
cast_add
cast_one
cast_to_int 📖mathematicalAddGroupWithOne.toIntCast
castZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
cast_zero
Int.cast_zero
cast_pos
PosNum.cast_to_int
cast_neg
Int.cast_neg
cast_zero 📖mathematicalcastZNum
ZNum
instZeroZNum
cast_zero' 📖mathematicalcastZNum
zero
cast_zneg 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
SubtractionMonoid.toSubNegMonoid
NegZeroClass.toNeg
ZNum
instNeg
neg_zero
neg_neg
cmp_to_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
cmp
PosNum.cmp_to_nat
Nat.instIsStrictOrderedRing
Int.instIsStrictOrderedRing
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
Int.instAddLeftMono
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
PosNum.cast_pos
lt_trans
neg_lt_zero
div_to_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
instDiv
div_zero
Num.cast_toZNum
Num.to_nat_to_int
PosNum.div'_to_nat
PosNum.cast_to_nat
Num.cast_toZNumNeg
PosNum.to_int_eq_succ_pred
PosNum.to_nat_to_int
Num.succ'_to_nat
Num.div_to_nat
PosNum.to_nat_eq_succ_pred
div_zero 📖mathematicalZNum
instDiv
instZeroZNum
dvd_iff_mod_eq_zero 📖mathematicalZNum
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
CommRing.toNonUnitalCommRing
commRing
instMod
instZeroZNum
dvd_to_int
mod_to_int
dvd_to_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
commRing
of_to_int
Int.cast_mul
mul_to_int
gcd_to_nat 📖mathematicalcastNum
Nat.instOne
MulZeroClass.toZero
Nat.instMulZeroClass
gcd
castZNum
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
Num.gcd_to_nat
abs_to_nat
isOrderedAddMonoid 📖mathematicalIsOrderedAddMonoid
ZNum
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
commRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
linearOrder
le_to_int
cast_add
add_le_add_left
covariant_swap_add_of_covariant_add
Int.instAddLeftMono
isStrictOrderedRing 📖mathematicalIsStrictOrderedRing
ZNum
CommSemiring.toSemiring
CommRing.toCommSemiring
commRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
linearOrder
IsStrictOrderedRing.of_mul_pos
isOrderedAddMonoid
zeroLEOneClass
nontrivial
lt_to_int
mul_to_int
cast_zero
mul_pos
IsStrictOrderedRing.toPosMulStrictMono
Int.instIsStrictOrderedRing
le_to_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
instLE
not_lt
lt_to_int
lt_to_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
instLT
cmp_to_int
not_lt_of_gt
mod_to_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
instMod
Num.cast_toZNum
Num.to_nat_to_int
cast_pos
Num.mod_to_nat
PosNum.to_nat_to_int
abs_to_nat
Num.cast_sub'
cast_neg
Num.succ_to_nat
PosNum.to_int_eq_succ_pred
mul_to_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
instMul
MulZeroClass.zero_mul
MulZeroClass.mul_zero
PosNum.cast_mul
neg_mul_eq_mul_neg
neg_mul_eq_neg_mul
neg_mul_neg
neg_of_int 📖mathematicalZNum
AddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
commRing
instNeg
Int.cast_neg
zneg_zneg
neg_zero 📖mathematicalZNum
instNeg
instZeroZNum
nontrivial 📖mathematicalNontrivial
ZNum
ofInt'_eq 📖mathematicalofInt'
ZNum
AddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
commRing
neg_neg
Nat.cast_succ
Num.add_one
Num.zneg_toZNumNeg
Num.toZNum_succ
add_one
ofInt'_neg 📖mathematicalofInt'
ZNum
instNeg
Num.zneg_toZNumNeg
Num.ofNat'_zero
Num.zneg_toZNum
of_intCast 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
ZNum
AddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
commRing
cast_to_int
to_of_int
of_natCast 📖mathematicalcastZNum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddGroupWithOne.toAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
NegZeroClass.toNeg
ZNum
AddMonoidWithOne.toNatCast
addMonoidWithOne
Int.cast_natCast
of_intCast
of_nat_toZNum 📖mathematicalNum.toZNum
Num
AddMonoidWithOne.toNatCast
Num.addMonoidWithOne
ZNum
addMonoidWithOne
of_nat_toZNumNeg 📖mathematicalNum.toZNumNeg
Num
AddMonoidWithOne.toNatCast
Num.addMonoidWithOne
ZNum
instNeg
addMonoidWithOne
of_nat_toZNum
Num.zneg_toZNum
of_to_int 📖mathematicalZNum
AddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
commRing
castZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Int.instRing
ofInt'_eq
of_to_int'
of_to_int' 📖mathematicalofInt'
castZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
Num.ofNat'_zero
cast_pos
PosNum.cast_to_nat
Num.ofInt'_toZNum
PosNum.of_to_nat
cast_neg
ofInt'_neg
to_int_inj 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
of_to_int'
to_of_int 📖mathematicalcastZNum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.instCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
ZNum
AddGroupWithOne.toIntCast
CommRing.toRing
commRing
Int.cast_zero
Int.cast_add
Int.cast_one
cast_add
AddRightCancelSemigroup.toIsRightCancelAdd
Int.cast_sub
cast_sub
zeroLEOneClass 📖mathematicalZeroLEOneClass
ZNum
instZeroZNum
instOneZNum
instLE
zero_add 📖mathematicalZNum
instAdd
instZeroZNum
zneg_bit1 📖mathematicalZNum
instNeg
bit1
bitm1
zneg_bitm1 📖mathematicalZNum
instNeg
bitm1
bit1
zneg_neg 📖mathematicalZNum
instNeg
neg
pos
zneg_pos 📖mathematicalZNum
instNeg
pos
neg
zneg_pred 📖mathematicalZNum
instNeg
pred
succ
zneg_zneg
zneg_succ
zneg_succ 📖mathematicalZNum
instNeg
succ
pred
succ.eq_3
Num.zneg_toZNumNeg
zneg_zneg 📖mathematicalZNum
instNeg

(root)

Definitions

NameCategoryTheorems
ZNum 📖CompData
48 mathmath: ZNum.neg_zero, ZNum.zeroLEOneClass, ZNum.zneg_succ, ZNum.of_nat_toZNumNeg, ZNum.cast_zneg, ZNum.of_natCast, ZNum.cmp_to_int, ZNum.of_intCast, ZNum.zneg_pos, ZNum.mod_to_int, ZNum.isOrderedAddMonoid, ZNum.cast_add, ZNum.cast_lt, ZNum.le_to_int, ZNum.neg_of_int, ZNum.cast_one, ZNum.zneg_bit1, PosNum.cast_to_znum, ZNum.zneg_pred, ZNum.bit0_of_bit0, ZNum.cast_le, Num.zneg_toZNumNeg, ZNum.to_of_int, ZNum.nontrivial, Num.succ_ofInt', ZNum.zneg_neg, ZNum.cast_zero, Num.add_toZNum, ZNum.dvd_iff_mod_eq_zero, ZNum.of_to_int, ZNum.div_zero, ZNum.cast_mul, ZNum.div_to_int, Num.zneg_toZNum, ZNum.lt_to_int, ZNum.of_nat_toZNum, ZNum.bit1_of_bit1, ZNum.ofInt'_neg, ZNum.dvd_to_int, ZNum.cast_sub, ZNum.zneg_bitm1, ZNum.zero_add, ZNum.mul_to_int, ZNum.isStrictOrderedRing, ZNum.add_zero, ZNum.add_one, ZNum.zneg_zneg, ZNum.ofInt'_eq

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